Torque Ontology

# Torque Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements/torque-ontology.html

FLOW TorqueOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Mechanical Measurements
    -> Torque Ontology

  PURPOSE:
    Represent torque as a measurable rotational mechanical quantity describing the turning effect of a force about a point, axis, or origin, including magnitude, direction, moment arm, units, dimensional structure, reference frames, rotational equilibrium, angular momentum, angular acceleration, measurement conditions, uncertainty, and mechanical interactions.

  ENTITY Torque {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: tau
    DIMENSION: M * L^2 * T^-2
    SI_UNIT: newton_metre
    SI_SYMBOL: N*m

    DEFINITION:
      torque := cross_product(PositionVector, Force)

    VECTOR_FORM:
      tau = r x F

    MAGNITUDE_FORM:
      |tau| = r * F * sin(theta)

    PERPENDICULAR_FORCE_FORM:
      |tau| = r_perpendicular * F

    PROPERTIES:
      has_magnitude
      has_direction
      has_unit
      has_dimension
      has_axis_or_origin
      has_point_of_application
      has_moment_arm
      has_reference_frame
      may_be_resultant
      may_be_balanced
      may_vary_with_time
      may_have_uncertainty
  }

  ENTITY Force {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: F
    DIMENSION: M * L * T^-2
    SI_UNIT: newton
    SI_SYMBOL: N

    RELATION:
      PositionVector cross Force -> Torque
  }

  ENTITY PositionVector {
    TYPE: VectorQuantity
    SYMBOL: r
    DIMENSION: L

    DEFINITION:
      vector_from_rotation_origin_or_axis_reference_to_force_application_point
  }

  ENTITY MomentArm {
    TYPE: LengthQuantity
    SYMBOL: r_perpendicular
    DIMENSION: L

    DEFINITION:
      perpendicular_distance_from_axis_to_force_line_of_action
  }

  ENTITY AngularMomentum {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: L
    DIMENSION: M * L^2 * T^-1

    RELATION:
      NetTorque = derivative(AngularMomentum, Time)
  }

  ENTITY AngularAcceleration {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: alpha
    DIMENSION: T^-2

    RELATION:
      NetTorque = MomentOfInertia * AngularAcceleration
      WHEN rigid_body_fixed_axis_conditions_apply
  }

  ENTITY MomentOfInertia {
    TYPE: RotationalInertiaQuantity
    SYMBOL: I
    DIMENSION: M * L^2

    RELATION:
      Torque = MomentOfInertia * AngularAcceleration
      UNDER applicable_rotational_conditions
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: newton_metre
      symbol: N*m

      equivalence:
        1 N*m = 1 kg*m^2/s^2
    }

    COMMON_ALTERNATIVES {
      kilonewton_metre
      newton_centimetre
      pound_force_foot
      pound_force_inch
    }

    SEMANTIC_UNIT_RULE:
      newton_metre_for_torque MUST_REMAIN_SEMANTICALLY_DISTINCT_FROM joule_for_energy
      DESPITE identical_base_dimensions

    CONVERSION_RULE:
      torque_value(target_unit)
        = torque_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by_system_role:
      applied_torque
      net_torque
      reaction_torque
      resisting_torque

    by_state:
      constant_torque
      variable_torque
      balanced_torque
      unbalanced_torque

    by_context:
      static_torque
      dynamic_torque
      motor_torque
      shaft_torque
      frictional_torque
  }

  RELATIONSHIPS {
    Torque -> CROSS_PRODUCT_OF -> PositionVector
    Torque -> CROSS_PRODUCT_OF -> Force
    Torque -> HAS_DIMENSION -> M*L^2*T^-2
    Torque -> MEASURED_IN -> NewtonMetre
    Torque -> ACTS_ABOUT -> AxisOrOrigin
    Torque -> DEPENDS_ON -> MomentArm
    NetTorque -> RATE_OF_CHANGE_OF -> AngularMomentum
    NetTorque -> MAY_PRODUCE -> AngularAcceleration
    MultipleTorques -> VECTOR_SUM_TO -> NetTorque
    BalancedTorques -> PRODUCE -> ZeroNetTorque
  }

  SEMANTIC_EQUIVALENCE {
    "torque" ~= "moment of force"
    "turning moment" ~= torque WHEN rotational_mechanics_context
    "N m" ~= "N*m"
    "newton metre" ~= torque_unit
    torque != force
    torque != energy
    torque != angular_momentum
    torque != moment_of_inertia
  }

  NET_TORQUE_MODEL {
    DEFINITION:
      NetTorque := vector_sum(all_external_torques_about_defined_origin_or_axis)

    FORM:
      tau_net = sum(tau_i)

    RULE:
      IF tau_net = 0
      THEN angular_momentum_is_constant
      ABOUT applicable_origin_or_axis
  }

  EQUILIBRIUM_MODEL {
    ROTATIONAL_EQUILIBRIUM:
      vector_sum(Torques) = 0

    STATIC_RIGID_BODY_EQUILIBRIUM:
      vector_sum(Forces) = 0
      AND vector_sum(Torques) = 0

    RULE:
      zero_net_torque alone DOES_NOT guarantee translational_equilibrium
  }

  CONSTRAINTS {
    torque_is_axial_vector_or_pseudovector_in_three_dimensional_classical_mechanics = true
    dimensional_formula = M*L^2*T^-2
    torque_requires_defined_origin_or_axis = true
    moment_arm_is_perpendicular_distance = true
    force_parallel_to_position_vector_produces_zero_torque = true
    maximum_torque_for_fixed_r_and_F_occurs_at_perpendicular_force = true
    torque_and_energy_are_not_semantically_equivalent = true
    net_torque_is_vector_sum = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Torque

    DIRECT_OR_INSTRUMENTAL_MEASUREMENT:
      torque_sensor
      torque_transducer
      torque_wrench
      dynamometer_with_rotational_measurement

    INDIRECT_MEASUREMENT:
      force_times_perpendicular_moment_arm
      cross_product_of_position_and_force
      moment_of_inertia_times_angular_acceleration
      angular_momentum_change_over_time

    RECORD:
      numerical_value
      unit
      vector_direction_or_axis
      force
      moment_arm
      angle
      point_of_application
      rotation_origin_or_axis
      timestamp
      reference_frame
      instrument
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_torque = best_estimate +/- measurement_uncertainty
  }

  REASONING_RULES {
    IF position_vector_known AND force_vector_known
      THEN torque = cross_product(position_vector, force)

    IF force_magnitude_known AND moment_arm_known
      THEN torque_magnitude = force * moment_arm

    IF r_known AND F_known AND angle_known
      THEN torque_magnitude = r * F * sin(angle)

    IF force_line_of_action_passes_through_axis
      THEN torque_about_axis = 0

    IF multiple_torques_act_about_same_origin_or_axis
      THEN net_torque = vector_sum(all_torques)

    IF net_torque = 0
      THEN angular_momentum = constant
      UNDER applicable_closed_system_conditions

    IF rigid_body_fixed_axis
      AND moment_of_inertia_constant
      AND net_torque_known
      THEN angular_acceleration = net_torque / moment_of_inertia

    IF net_torque_known_as_function_of_time
      THEN angular_momentum_change = integral(net_torque, time)
  }

  VECTOR_MODEL {
    torque_vector:
      tau = r x F

    cartesian_components:
      tau_x = r_y*F_z - r_z*F_y
      tau_y = r_z*F_x - r_x*F_z
      tau_z = r_x*F_y - r_y*F_x

    magnitude:
      |tau| = r*F*sin(theta)

    direction:
      determined_by_right_hand_rule
  }

  REFERENCE_MODEL {
    torque_value DEPENDS_ON chosen_origin_or_axis

    REQUIRE:
      identify_origin_or_axis
      identify_force_application_point
      identify_force_direction

    RULE:
      torque_values_about_different_origins_or_axes
      MUST_NOT be combined without transformation_or_recalculation
  }

  ROTATIONAL_DYNAMICS_MODEL {
    GENERAL_RELATION:
      tau_net = dL/dt

    FIXED_AXIS_RIGID_BODY_CASE:
      tau_net = I*alpha
      WHEN moment_of_inertia_is_constant_about_axis

    ANGULAR_IMPULSE:
      integral(tau_net, dt) = delta_L
  }

  WORK_ENERGY_DISTINCTION {
    torque_unit:
      N*m

    energy_unit:
      J

    dimensional_equivalence:
      dimension(Torque) = dimension(Energy)

    semantic_distinction:
      Torque represents rotational tendency
      Energy represents capacity for work or transferred work

    RULE:
      DO_NOT automatically convert torque N*m into joules
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    rotational_relationship_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when force direction, moment arm, angle,
      origin, axis, point of application, reference frame,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK origin_or_axis_definition
    CHECK force_direction
    CHECK moment_arm_geometry
    CHECK vector_cross_product_orientation
    CHECK right_hand_rule_consistency
    CHECK torque_energy_semantic_distinction
    CHECK rotational_model_assumptions
    CHECK instrument_calibration_when_measured
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      validate_axis_or_origin
      validate_force_and_moment_arm
      normalize_to_canonical_unit
      preserve_original_value_and_unit
      attach_timestamp
      attach_point_of_application
      attach_uncertainty
      update_torque_state

    ON force_or_geometry_change:
      update_position_vector
      update_force_vector
      recompute_individual_torque
      recompute_net_torque
      update_rotational_state

    ON revised_calibration:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Torque
    canonical_symbol: tau
    canonical_dimension: M*L^2*T^-2
    canonical_SI_unit: N*m

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_force
      identify_position_vector_or_moment_arm
      identify_angle
      identify_origin_or_axis
      identify_direction
      identify_point_of_application
      identify_reference_frame
      identify_rotational_dynamics_context
      identify_measurement_method
      identify_uncertainty
      validate_dimensions
      infer_relationships

    ambiguity_controls:
      distinguish_torque_from_force
      distinguish_torque_from_energy
      distinguish_torque_from_angular_momentum
      distinguish_torque_from_moment_of_inertia
      distinguish_individual_torque_from_net_torque
      distinguish_moment_arm_from_radial_distance
      distinguish_origin_dependent_torque_values
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_mechanical_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Mechanical Measurements
      -> Torque Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      net_torque_model
      equilibrium_model
      rotational_dynamics_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      constraint_model_changes
      rotational_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW